I'm not against the money of shirt sponsors as long as it doesn't give too much money. It should be done like the advertising boards and increase as you go up. Would reach something like 50k max for A div teams in official matches. Friendlies the sponsor would give a quarter of the amount.

Just another idea, perhaps you have to earn sponsorship? Companies won't just go out and sponsor a small team, they'd go and sponsor a big club, so it could work that you gain sponsorships based on division and manager points? This way my previous example works, but it would help decrease inflation as not every new team can come into the game and gain free money, they'd have to work for it a bit before they can earn a sponsor.